Seminaire de Geometrie Algebrique (SGA): English Translation Working Drafts

Public SGA working-translation record for the Modern LaTeX Editions of Mathematics Manuscripts project. This record keeps reader-facing PDFs, source-scan witnesses, and compact source ZIPs for SGA translation/reconstruction work. Audit caveat, 2026-06-09: the SGA5 and SGA6 page-range chains are structurally represented and mathematically useful, but they should be treated as substantial working drafts rather than scribe-grade complete editions. Some uploaded filenames still contain earlier labels such as complete or source-checked; those labels should be read together with this caveat and the current audit notes. Current SGA5 status. This version carries forward repair006, repair007, and repair008, and adds sga5_repair009_20260609.zip. repair009 is a targeted French cumulative operator-symbol repair pass over repair008, not a global certification. It converts source-visible internal Hom/RHom notation in Expose III and III B to underlined operator forms where patched, with repaired pages 123, 141, 166, 167, 175, and 179. English is included only as an unsynchronized repair002 carry-forward. Repair008 and repair009 specifics. repair008 closed source-witnessed French diagram/formula issues on source pages 083, 095, 098, 100, 116, and 184, with pages 326 and 457 dispositioned as checked/no-patch in that lane. repair009 then focuses on internal Hom/RHom typography and notation in Expose III/III B: it replaces patched raw RHom/Hom forms with source-visible underlined operator macros and inventories remaining raw tokens outside the patched scope for page-local checking. Both packages include cumulative French TeX/PDF, source witnesses, crops or ledgers, render checks, and audit notes. Open SGA5 lanes. SGA5 French still requires full page-by-page source-vs-TeX certification. Raw Hom/RHom/Ext/H operator typography outside the patched Expose III/III B lane still needs systematic checking. Diagrams outside the repair witness lanes still require source/current comparison. The English cumulative must be regenerated from the corrected French once the French branch is canonical. Current SGA6/SGA7 status. SGA6 is structurally covered across the source range, but the audit confirms localized compression/omission samples on source pages 014 and 625, with strong candidates on 431 and 679. Next repair targets remain p014, then clusters 423-454, 619-653, and 670-692. SGA7-I material is staged only as working draft material unless a specific packet declares source-checked coverage. Corrections, exact source comparisons, LaTeX fixes, and promoted replacement ranges can be suggested through GitHub issues or pull requests: https://github.com/KokunoYumeto/modern-latex-manuscripts.